Kalman and Pugachev filters are the basis of modern methods of operative information processing. I will present an introduction to the theory of stochastic systems, an introduction to the theory of linear estimation (filtration) of processes in continuous and discrete stochastic systems based on Kalman filters and its generalizations (Pugachev filter). In addition, a filter based on modified Haar wavelets is considered. Examples are given.

Gravitational-wave detection efforts focus on four frequency bands: (i) The extremely low frequency (ELF) band, 10⁻¹⁵to 10⁻¹⁸Hz, in which waves will be sought via their imprint on the polarization of the cosmic microwave

background (CMB) radiation, and the only expected source is primordial gravitational fluctuations amplified by inflation of the universe. (ii) The very low frequency (VLF) band, 10⁻⁷to 10⁻⁹Hz, in which the waves are sought

using high-stability pulsar timing, and the expected sources are processes in the very early Universe and extremely massive binary black hole systems. (iii) The low frequency (LF) band, 10⁻⁴Hz, in which LISA will operate,

and (iv) the high frequency (HF) band, 10 to 10⁴Hz, in which earth-based detectors (interferometers and resonant-mass detectors) operate. The physical principles and current sensitivity of these detectors are briefly  discussed.

The discovery of gravitational waves by the LIGO collaboration, in addition to probing gravity in an extreme regime, has also opened a new window to the Universe. It allows us to investigate the final stage of massive stars and compact objects. The first detected event, GW150914, was resulted from the merger of two massive black holes. Here we discuss the theory of gravitational waves and astrophysical sources which can shed light to our  understanding of the Universe.